The probability plot correlation coefficient (PPCC) plot can be used to
determine the optimal shape parameter for a one-parameter family of
distributions. It cannot be used for distributions without shape parameters
(like the normal distribution) or with multiple shape parameters.

By default a Tukey-Lambda distribution (stats.tukeylambda) is used. A
Tukey-Lambda PPCC plot interpolates from long-tailed to short-tailed
distributions via an approximately normal one, and is therefore particularly
useful in practice.

Parameters:

x : array_like

Input array.

a, b: scalar

Lower and upper bounds of the shape parameter to use.

dist : str or stats.distributions instance, optional

Distribution or distribution function name. Objects that look enough
like a stats.distributions instance (i.e. they have a ppf method)
are also accepted. The default is 'tukeylambda'.

plot : object, optional

If given, plots PPCC against the shape parameter.
plot is an object that has to have methods “plot” and “text”.
The matplotlib.pyplot module or a Matplotlib Axes object can be used,
or a custom object with the same methods.
Default is None, which means that no plot is created.

N : int, optional

Number of points on the horizontal axis (equally distributed from
a to b).

Now we explore this data with a PPCC plot as well as the related
probability plot and Box-Cox normplot. A red line is drawn where we
expect the PPCC value to be maximal (at the shape parameter -0.7 used
above):